Freestyle is not exporting with the object
As mentioned in the comments the cartoon-style black outline is an image only effect done internally in post production over the rendered image, it does not affect the model nor is it part of the geometry, there fore it cannot be exported in any file format other than a rendered image, or at best as an SVG vector file (using the Freestyle SVG Exporter addon), you can then place over your image.

Where are you exporting your model in COLLADA too? Some Game engine? Other modelling application? You will most likely need to recreate the outline effect there in the destination software.

Otherwise if you actually want to have it in-model with actual geometry there are a few other options.


Either us a wireframe modifier over your objects to construct a cage-like structure over you mesh
Use a Bevel modifier on your mesh with a material index offset

Manually bevel your geometry and assign different materials
UV Unwrap your model and use an image texture, created in an external image editing software with the desired black edges in the correct places along the edges.